A man is three times as old as his son was at the time when the father was twice as old as his son will be two years from now. Find the
present age of each if they sum to 55.
Answers
Answer:
answer is int he explanation
Step-by-step explanation:
Let f = Father's age now
Let s = Son's age now
given:
f+%2B+s+=+55
The Son's age in 2 years is
s+%2B+2
When the Father was twice as old as the Son will be in two years is
2%2A%28s+%2B+2%29
How old was the Son then?
The difference in their ages is a constant
f+-+s+=+c
s+=+f+-+c
2%2A%28s+%2B+2%29+-+c
2s+%2B+4+-+c
The Father's present age is three time the Son's at that time
f+=+3%2A2%2A%28s+%2B+2%29+-+3c
(1) f+=+6s+%2B+12+-+3c
also,
(2) f+%2B+s+=+55
(3) f+-+s+=+c
Substitute (3) in (1)
(1) f+=+6s+%2B+12+-+3%2A%28f+-+s%29
(1) f+=+6s+%2B+12+-+3f+%2B+3s
(1) 4f+-+9s+=+12
Multiply both sides of (2) by 4 and
subtract (1) from (2)
(2) 4f+%2B+4s+=+220
(1) -4f+%2B+9s+=+-12
(3) 13s+=+208
(3) s+=+16
and, since
(2) f+%2B+s+=+55
(2) f+=+55+-+16
(2) f+=+39
The father is 39 now, and the Son is 16
----------------------------------------
check answer:
The Son's age in 2 years is
16+%2B+2+=+18
When the Father was twice as old as the Son will be in two years is
2%2A%2816+%2B+2%29
36
How old was the Son then?
The difference in their ages is a constant
36+-+s+=+c
s+=+36+-+c
2%2A%28s+%2B+2%29+-+c
2s+%2B+4+-+c
The Father's present age is three time the Son's at that time
39+=+3%2A2%2A%28s+%2B+2%29+-+3c
(1) 39+=+6%2A16+%2B+12+-+3c
(1) 39+=+96+%2B+12+-+3c
(1) 3c+=+96+%2B+12+-+39
(1) 3c+=+108+-+39
(1) 3c+=+69
(1) c+=+23
and
(3) f+-+s+=+c
(3) 39+-+16+=+23